Information geometry of hyperbolic-valued Boltzmann machines

Information geometry is a useful tool for analysis of neural networks. In this work, information geometry is introduced to analysis of hyperbolic-valued neural networks. First, hyperbolic-valued Boltzmann machines (HBMs) are organized. Next, the HBMs are analyzed as a neuro manifold from standpoint of information geometry. We prove that the HBMs form an exponential family and provide the natural and mixture parameters. Moreover, the Fisher metric is determined. In addition, we prove the existence of mixed parameters for all the distributions, which are useful for learning algorithms. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

Information geometry is introduced to analyze hyperbolic-valued neural networks, proving that they form an exponential family and providing natural and mixture parameters, determining the Fisher metric, proving the existence of mixed parameters for all distributions, which are useful for learning algorithms.